How does a voltage doubler work?

We're told that, with the jumper inserted, the output voltage is about twice as great as without the jumper. We didn't need to prove this theoretically, but for my own curiosity, I was wondering if someone could give a clear, thorough explanation of why this works. When I search online, I see circuits that are similar but not quite the same, and kind of short answers that I don't quite understand. Thanks!